PSI - Issue 2_B

Manuela Sander et al. / Procedia Structural Integrity 2 (2016) 034–041 M. Sander et al./ Structural Integrity Procedia 00 (2016) 000–000

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1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 1.0E+05 1.0E+06 1.0E+07 1.0E+08 1.0E+09 σ a / σ th  σ a / σ th N f (log) FELIX 10-641 FELIX 11-641 FELIX 12-641 FELIX 10-705 CA (R = -1) a)

FELIX 10-641 FELIX 11-641 FELIX 12-641 FELIX 10-705 CA (R = -1)

Felix 10

100 120 140 160

Felix 11

0 20 40 60 80

√ area [µm]

Felix 12

1.0E+05 1.0E+06 1.0E+07 1.0E+08 1.0E+09

b)

N f (log)

Fig. 6. (a) Modified S-N curves and (b) the defect size for Felix in comparison to constant amplitude test results with R = -1 (Müller (2016)).

The results of the different experiments with Felix are shown in Fig. 6a in comparison to constant amplitude test results with R = -1 in terms of the modified S-N curve. It becomes obvious that the different reconstructions of the load spectrum have nearly no influence, but the modified S-N curve is shifted to higher lifetimes in comparison to the constant amplitude tests. The inclusion sizes, at which the cracks initiate in constant amplitude tests, lead to higher failure cycles at variable amplitude loading. Moreover, the inclusion sizes decrease with increasing failure cycles. In contrast, the values of √ area are almost independent of N f for constant amplitude loading. Moreover, due to the variable amplitude loading arrest marks are visible around the inclusion in and outside the fish-eye (Fig. 7). Depending on the reconstruction of the load spectrum the size and the area, where arrest marks are observable, as well as the spacings between the arrest marks are different.

a)

b)

c)

1000 µm

1000 µm

1000 µm

400 µm

400 µm

500 µm

Fig. 7. Fracture surfaces with arrest marks within the fish-eye around non-metallic inclusions from experiments with a) Felix 10, b) Felix 11 and c) Felix 12 (Müller, Sander (2013))

The S-N curve and the modified S-N curve of the experiments with the standardized load sequence WISPER are compared with the results of constant amplitude tests with R = 0 in Fig. 8. While the S-N curve (Fig. 8a) is shifted to higher lifetimes, the modified S-N curves of the constant and variable amplitude loading (Fig. 8b) collapse nearly to one curve. Under the assumption that an arrest mark occurs, if one sequence ends after 2,276,625 cycles in the case of Felix/28 and another sequence starts, the arrest marks can be counted and related to the loading. For each arrest mark an appropriate cyclic stress intensity factor is calculated using the √ area -approach and an average stress amplitude, which is weighted with the number of cycles of each class. By measuring the arrest marks (Fig. 9b) an average crack growth rate da/dN has been calculated, which is related to an average cyclic stress intensity factor corresponding to two adjacent arrest marks. The results depending on the load sequences are shown in Fig. 9a. It becomes obvious that all determined values are below the long crack growth threshold, but almost all above the short crack growth threshold calculated with the Newman/NASA approach (NASA (2009) and Newman (1999)).